Re: Is simplification possible (how to know)?

Rewrite your function as
Let be a function of x and y which is a multinomial (does not have square roots in it). (Note that might equal zero or some other constant)
If that function does factorise then it can be written as

From this you can determine that

and

From:
You can determine that and

h(x,y) is simple enough that you can tell it cannot be factored any more (Well actually can be factorised but it involves imaginary numbers so ignore that)

Since
You can rewrite that as

You know g(x,y) and so you can do the long division. When you do the long division you will get a remainder. The remainder is equal to

That's as much progress as I can make towards getting the factors. Maybe you can work out the next step. This is very involved for pre-university maths.